Capacity inequalities and Lipschitz continuity of mappings

TL;DR

This paper investigates the properties of topological mappings constrained by p-capacity inequalities, establishing Lipschitz continuity for the case p=n-1, thereby extending previous mathematical results.

Contribution

It extends Gehring's result by proving Lipschitz continuity of mappings defined by p-capacity inequalities specifically when p equals n-1.

Findings

Lipschitz continuity holds for mappings with p-capacity inequalities when p=n-1

Extension of Gehring's result to a broader class of mappings

Provides new insights into the regularity of topological mappings

Abstract

In this paper we consider topological mappings defined by $p$-capacity inequalities in domains of $\mathbb R^n$. In the case $p=n-1$ we prove the Lipschitz continuity of such mappings, that extends the result by F.~W.~Gehring.